I wonder if this is the majority view? I hear it often but it's not something I feel (disclosure: I have one child).
I certainly think in terms of leaving the world better for all living things rather than for my children (although I guess they would benefit).
I personally feel shame that I am a part of the destruction of this world which in turn motivates me to want to make it better.
This is something that has grown as I have aged, I feel now that I'm older I can see things in the longer term and I can see how long it takes to make change and make it stick.
In general, it is procreation that makes humans think about the long term. The truth is, no matter what you do, you will be dead in a hundred years. Wanting to leave the world a better place for your children and grand-children is a much more powerful motivator than abstract philosophical principle.